Diffusion length scale

A First Glimpse at Turbulent Diffusion Diffusion Length Scales Dispersion... 

Figure 2.45 Extended plating in an SPS-CI-PEG electrolyte yields a smooth, bright surface on the sub-1 pm length scale through the CEAC mechanism. However, coupling with the density driven convective flow fields leads to pattern formation on the diffusive length scale of 100 pm. The addition of a leveler helps attenuate the latter effect (not shown).

Figure 3-11. (a) The velocity profiles at various increasing times above an infinite flat plate that suddenly begins moving in its own plane at t = 0 with a constant velocity U (the Rayleigh problem), (b) The selfsimilar velocity profile for the same problem obtained by the rescaling of the distance from the plate y with the diffusion length scale Jvt for all t > 0. 

This equation shows that vorticity is a maximum at the moving wall (which acts a source of vorticity) and decays exponentially on a length scale 0(l/Re) by the action of viscous forces. Thus for Rey 1 the flow is effectively irrotational. In this respect the problem is atypical as we normally expect vorticity to decay on a diffusive length scale of 0( / J Re) (cf. oscillatory Couette flow). The reason for this difference is that in the present probiem we have a balance between convective inertia and viscous forces as opposed to a balance between transient inertia and viscous forces. 

Within the shallow crust, the diffusive length-scale of He relative to the rate of groundwater flow can be a significant factor in modeling noble gas loss from aquifer systems to the atmosphere. For example, loss by diffusion to the atmosphere can be modeled assuming a zero concentration boundary at the surface and a zero concentration initial condition (Andrews et al. 1989a) ... 

Fig. 11. The inadequacy of diffusive mixing, even after geological time periods, (a) Very poor mixing in a thin reservoir because the diffusive length scale L is small relative to the lateral extent of the reservoir. (Deff> effective diffusion coefficient, m /s t, time period, s). (b) Moderate diffusive mixing in a thick gross reservoir. The small inset figures show generalized API gravity and/or GOR, and bubble point and reservoir pressure depth trends...

In general it is clear that PFG spin-echo data can provide information on the pore structure at both the gradient length scale, /q, and the diffusion length scale, y (/JA). The NMR data can be analysed to obtain simple structure factors, which may then be related to particular pore network models. ... 

White and coworkers have recently described an experimental approach in which intramonomer spin-diffusion is used to quantitatively define upper limits on the value of spin-diffusion coefficients D in mobile and rigid homopolymers, as well as in copolymers and blends [61-63]. The independent determination of the diffusion coefficient using only NMR data would be possible if a unique, invariant reference volume or distance existed in the polymer sample that could be used to quantitatively define the diffusive length scale. In other words, an internal distance calibration on the sample itself would eliminate the need for independent... 

Figure 3-26 H(log s), which represents the spectrum of diffusive length scales, is shown for n = 1-11 for Re = 10(10). The scale distributions in the main panel of each figure approach an invariant distribution as the period increases. The inset reveals the broadening distributions as striations are created by the flow.

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